Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00135673" target="_blank" >RIV/00216224:14310/24:00135673 - isvavai.cz</a>

Result on the web

<a href="https://www.worldscientific.com/doi/10.1142/S0219199723500141" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0219199723500141</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219199723500141" target="_blank" >10.1142/S0219199723500141</a>

Result language

angličtina

Original language name

Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers

Original language description

Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally invariant differential operator, intrinsically defined on a conformal manifold, mapping scalars to scalars. This operator is a special case of the so-termed extrinsic Paneitz operator defined in the case when the conformal manifold is itself a conformally embedded hypersurface. In particular, this encodes the obstruction to smoothly solving the five-dimensional scalar Laplace equation, and suitable higher dimensional analogs, on conformally compact structures with constant scalar curvature. Moreover, the extrinsic Paneitz operator can act on tensors of general type by dint of being defined on tractor bundles. Motivated by a host of applications, we explicitly compute the extrinsic Paneitz operator. We apply this formula to obtain: an extrinsically-coupled Q-curvature for embedded four-manifolds, the anomaly in renormalized volumes for conformally compact five-manifolds with negative constant scalar curvature, Willmore energies for embedded four-manifolds, the local obstruction to smoothly solving the five-dimensional singular Yamabe problem, and new extrinsically-coupled fourth- and sixth-order operators for embedded surfaces and four-manifolds, respectively.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Communications in Contemporary Mathematics

ISSN

0219-1997

e-ISSN

1793-6683

Volume of the periodical

26

Issue of the periodical within the volume

05

Country of publishing house

SG - SINGAPORE

Number of pages

50

Pages from-to

1-50

UT code for WoS article

001157533200001

EID of the result in the Scopus database

2-s2.0-85170275966